To find the length of the minor arc SV in circle [tex]\( T \)[/tex] with radius 24 inches and central angle [tex]\(\theta = \frac{5\pi}{6}\)[/tex] radians, we use the formula for arc length:
[tex]\[ \text{Arc Length} = \theta \times \text{Radius} \][/tex]
Step-by-step, let's proceed:
1. Identify the given values:
- Radius, [tex]\( r = 24 \)[/tex] inches
- Central angle, [tex]\( \theta = \frac{5\pi}{6} \)[/tex] radians
2. Substitute the values into the formula:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 24 \][/tex]
3. Multiply the constants:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 24 = 20\pi \][/tex]
So, the length of the minor arc SV is:
[tex]\[ 20\pi \text{ inches} \][/tex]
This matches one of the given options.
[tex]\[
\boxed{20\pi}
\][/tex]
